Yes, when I insert the natural sign from the Times Scale Degrees font directly into the text frame using "Insert > Glyph", it displays correctly and also exports to PDF correctly. I am perfectly happy with the way this works.
However, if I edit the text frame in the Story Editor and change the Style of the paragraph containing the inserted natural-sign glyph, the glyph will revert to the forward slash which occupies that position in other fonts.
I don't consider this a problem, since I have a working solution, and I just change it back in the text frame. I am always all in favor of the workaround that works the quickest. From the POV of you all, the intrepid programmers, this may be a problem in the Scribus code; to me, it's a problem solved.
I suggest that the OP might try inserting the problem "down-bow" glyph of the original post directly into the text frame instead of using the Story Editor, as a simple test, before seeking more elaborate solutions. It would be perfectly reasonable to do most of the editing in Story Editor as usual, and only add the glyph afterwards directly into the text frame when everything else is in order. If it works, great. If not, ehhh, on to the next idea.
Since the OP insists that other programs use the font, and since he or she clearly said that the problem occurred when using the Story Editor, I think that my experience with the natural-sign glyph also not showing correctly when inserted in the Story Editor, might be relevant and might provide a solution which will work even if it does not solve the issue on a programming level.
As a musician, I observe that there have been various issues that have arisen between Scribus and music notation programs in general, since staff notation is a specialized non-text symbolic language which in my experience is best treated in Scribus with imported image files. There are a lot of fonts that attempt to make musical symbols into text, and some are better than others. "Lilypond Book" is the program that, ideally, totally bridges that gap, but Scribus regardless of its faults is infinitely easier to learn to use than Lilypond.